Skip to main content

Full text of "Text Book Of Mechanical Engineering"

See other formats

Elastic Moduli;


origin from which stresses are measured along o A, and strains
along OB. E is the elastic limit and o E is a straight line, shewing
proportionality of the co-ordinates. Plasticity begins at E, and
(assuming a case of tensile stress) increases in perfection up to B,
the curve being interrupted at Y, the yielding or breaking-down
point (or commercial elastic limit), while the lowering at B s in-
dicates rapid contraction of sectional area at rupture (see A, Fig.
320). If the stress be compressive the material enlarges in
diameter after B is reached, and thus becoming stronger, the curve
rises thence instead of falling: neither is the yield point observed.

If W = load in tons at B, a = original area, and al = con-
tracted area :

W -5- a = stress per sq. in. estimated on original area.

and   W~tfx= stress per sq. in. estimated on contracted area.

The first is used commercially, and is shewn at B, while the latter,

the strictly scientific result, is given at BX ; and the plastic curve is

thus corrected.    The curve from B to s is not considered reliable.

Compressive stresses do not materially distort the specimen
up to B, so the curve requires no correction. The primitive
elastic limit occurs at E, after which a permanent set is given to
the bar. This limit may be altered artificially. (See p. 385.)

Modulus  of  Direct Elasticity, or Young's * modulus.
(E) is a number giving the ratio of stress and strain within the
elastic limit, and is practically the same for tension or compression
stress sq. in. in Ibs '     /tlbs    /clbs
strain per inch length ~~  St  .     Sc '

Modulus  of Transverse   Elasticity,   or Modulus of
Rigidity (C), serves similarly for shear action thus:
shear stress sq. in. in Ibs.      j^lbs



C = -

shear strain per inch length
if will be understood by reference to Fig. 322, .being the strain
between two shear planes am inch apart.

Modulus of Volumetric Elasticity (K) compares stress
and diminution in volume, thus:

stress sq. in. in Ibs.            fvM

53 decrease in vol. per cub. inch      3V

* Dr. Tto* Young, Foreign Sec. Royal Society) 1826.